Malik is comparing 2 right triangles. Both triangles have a hypotenuse of 13 units. The first triangle has a leg of 12 units and the other triangle has a leg of 5 units. How could Malik prove that the two triangles are congruent?(1 point) Responses He can conclude that they are congruent because they are both right triangles. He can conclude that they are congruent because they are both right triangles. He could apply the concept of HL and show that the two triangles are congruent. He could apply the concept of HL and show that the two triangles are congruent. He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent. He could apply the Pythagorean Theorem to show that the two missing sides make both triangles congruent. He would need additional information to prove that the two triangles are congruent.

Answer 1

Malik could prove that the two triangles are congruent by applying the concept of HL (Hypotenuse-Leg) congruence. The HL theorem states that two right triangles are congruent if their hypotenuses and one corresponding leg are equal.

In this case:

• Both triangles have the same hypotenuse length of 13 units.

• The first triangle has a leg of 12 units; to find its other leg, we can use the Pythagorean theorem: \[ a^2 + b^2 = c^2 \quad \text{(where } c \text{ is the hypotenuse)} \] Letting \( b \) be the leg length that we need to find: \[ 12^2 + b^2 = 13^2 \ 144 + b^2 = 169 \ b^2 = 25 \ b = 5 \] So, the first triangle has legs of 12 and 5.

• The second triangle has a leg of 5 units, and its hypotenuse is also 13 units.

Since both triangles have the same hypotenuse of 13 units and one leg (5 units), Malik can conclude that the two triangles are congruent by the HL theorem.

Therefore, the correct response is: He could apply the concept of HL and show that the two triangles are congruent.